Second order estimates for fully nonlinear elliptic equations with gradient terms on Hermitian manifolds

2021/08/06 by Bo Guan, Guan, Bo, Xiaolan Nie +1
Mathematics · #35J15 #35J60 #53C21 #53C55 #58J05 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2108.03308

openalex publication_date 2021/08/06 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28

Abstract

We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global estimates we obtained apply to an equation arising from a conjecture by Gauduchon which extends the Calabi conjecture; this was one of the original motivations to this work. We were also motivated by the fact that there had been increasing interests in fully nonlinear pde's from complex geometry in recent years, and aimed to develop general methods to cover as wide a class of equations as possible.

Citations

• (1,1) forms with specified Lagrangian phase: A priori estimates and\n algebraic obstructions
• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
• Global C2‐Estimates for Convex Solutions of Curvature Equations
• Nakai-Moishezon criterions for complex Hessian equations

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• The Dirichlet Problem of Fully Nonlinear Equations on Hermitian\n Manifolds
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• On a class of fully nonlinear elliptic equations on closed Hermitian manifolds